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Let veca , vecb , vecc be three unit vec...

Let `veca , vecb , vecc` be three unit vectors such that ` |veca + vecb +vecc| =1 and veca bot vecb , " if " vecc` makes angles ` delta beta " with " veca, vecb` respectively, then ` cos delta + cos beta ` is equal to

A

1

B

-1

C

`3/2`

D

0

Text Solution

Verified by Experts

The correct Answer is:
B
we have ` veca bot vecb` , therefore, ` veca.vecb =0`
Also, `vecc. Veca = cos delta and vecc. Vecb =cos beta` .
now , ` |veca + vecb + vecc|= 1`
`Rightarrow |veca + vecb + vecc|^(2) =1`
` Rightarrow |veca|^(2) + |vecb|^(2) + |vecc|^(2) + 2 (veca.vecb + vecb.vecc + vecc.veca) =1`
` Rightarrow 1+1+1+2 ( cos delta + cos beta) =1`
` Rightarrow cos delta + cos beta = -1`
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